MinT - Best Known (103−48, 103, s)-Nets in Base 5

Best Known (103−48, 103, s)-Nets in Base 5

(103−48, 103, 104)-Net over F₅ — Constructive and digital

Digital (55, 103, 104)-net over F₅, using

1 times m-reduction [i] based on digital (55, 104, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 52, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]

(103−48, 103, 135)-Net over F₅ — Digital

Digital (55, 103, 135)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−48, 103, 2431)-Net in Base 5 — Upper bound on s

There is no (55, 103, 2432)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 987192 815771 900940 593807 557733 634536 559670 338007 353345 973317 504048 513025 > 5¹⁰³ [i]